A 2 m ladder leans against a vertical wall.

Question

A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate
25 cm/sec, then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the
horizontal ground when the top of the ladder is 1 m above the ground is :

Accepted Answer

x2 + y2 = 4 $$ \Rightarrow $$ $$2x{{dx} \over {dt}} + 2y{{dy} \over {dt}} = 0$$

$$ \Rightarrow {{dx} \over {dt}} =  - {y \over x}.{{dy} \over {dt}}$$

When upper end is 1m above the ground, $${{dx} \over {dt}} =  - {1 \over {\sqrt 3 }}.25 =  - {{25} \over {\sqrt 3 }}$$ cm/sec.

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